Asymptotic Stability of a Stationary Solution to a Thermal Hydrodynamic Model for Semiconductors
Asymptotic Stability of a Stationary Solution to a Thermal Hydrodynamic Model for Semiconductors
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DOI：
10.1007/s00205-008-0129-1
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发表时间：
2009-05
影响因子：
2.5
通讯作者：
S. Nishibata;Masahiro Suzuki
中科院分区：
文献类型：
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作者：
S. Nishibata;Masahiro Suzuki
本文研究半导体一维导热流体动力学模型初始边值问题的平稳解的存在性和渐近稳定性。分析热对半导体器件中电子运动的影响对于通过处理热载流子问题来提高器件的可靠性具有重要意义。我们通过使用 Leray-Schauder 和 Schauder 不动点定理证明了满足亚音速条件的平稳解的唯一存在性。然后通过时间一致的先验估计证明了平稳解的渐近稳定性。在这里，能量形式起着至关重要的作用。我们还证明，随着时间趋于无穷大，解收敛到平稳解的速度呈指数级增长。
The present paper concerns the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for a one-dimensional heat-conductive hydrodynamic model for semiconductors. It is important to analyze thermal influence on the motion of electrons in semiconductor device to improve the reliability of devices by handling a hot carrier problem. We show the unique existence of the stationary solution satisfying a subsonic condition by using the Leray–Schauder and the Schauder fixed-point theorems. Then the asymptotic stability of the stationary solution is proved by deriving the a priori estimate uniformly in time. Here an energy form plays an essential role. We also prove that the solution converges to the stationary solution exponentially fast as time tends to infinity.